<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />

# 8.1: What's the Value

Difficulty Level: At Grade Created by: CK-12

Look at the equation below. Can you figure out the value of z\begin{align*}z\end{align*}? In this concept, we will learn how to use the order of operations to help us to solve equations.

6×32÷2+z+4(73)+23÷4=32×6+1

### Guidance

The order of operations tells us the correct order of evaluating math expressions. We always do parentheses first and then exponents. Next we do multiplication and division (from left to right) and finally addition and subtraction (from left to right).

In order to evaluate expressions using the order of operations, we can use the problem solving steps to help.

• First, describe what you see in the problem. What operations are there?
• Second, identify what your job is. In these problems, your job will be to solve for the unknown.
• Third, make a plan. In these problems, your plan should be to use the order of operations.
• Fourth, solve.
• Fifth, check. Substitute your answer into the equation and make sure it works.

#### Example A

Follow the order of operations and show each step. What is the value of the variable?

b+2×3×22÷3=2(5+6)2\begin{align*} b + 2 \times 3 \times 2^2 \div 3 = 2(5 + 6) - 2\end{align*}

Solution:

We can use the problem solving steps to help us with the order of operations.

#### Example B

Follow the order of operations and show each step. What is the value of the variable?

\begin{align*}10^2 - 6(4 + 6) - 3^2 - 3 \times 4 - 1 = d + 50 \div 5^2\end{align*}

Solution:

We can use the problem solving steps to help us with the order of operations.

#### Example C

Follow the order of operations and show each step. What is the value of the variable?

\begin{align*}4(9 - 5) + h + 3^2 - 2^3 + 4^1 = 3^2 \times 3 - 2 \times 3\end{align*}

Solution:

We can use the problem solving steps to help us with the order of operations.

#### Concept Problem Revisited

We can use the problem solving steps to help us with the order of operations.

### Vocabulary

The order of operations tells us the correct order of evaluating math expressions. We always do parentheses first and then exponents. Next we do multiplication and division (from left to right) and finally addition and subtraction (from left to right).

### Guided Practice

For each problem, follow the order of operations and show each step. What is the value of the variable?

1. \begin{align*}2 + 5^2 \div 5 \times 1 + 0 \times 34 = 2y - 7(4 - 3)\end{align*}

2. \begin{align*}2a + 5(9 - 8) \times 2^2 = 2^2 \times 3^2 + 2\end{align*}

3. \begin{align*}9^2 - 8^2 - 16 + 4^3 + 2^2 = e(5 + 2) - 1\end{align*}

1. Here are the steps to solve:

2. Here are the steps to solve:

3. Here are the steps to solve:

### Explore More

For each problem, follow the order of operations and show each step. What is the value of the variable?

1. \begin{align*}2m + 3 \times 9 \div 3^3 + 4(8 - 3) = 7^2 - 3 \times 6\end{align*}
2. \begin{align*}7^2 \div 7 \times (5^2 - 17) - (2 \times 6) = 4l - 2^2 \times 5\end{align*}
3. \begin{align*}6+3^2 \div 3 \times 2 +1 \times 5 =3y-2(5-3)\end{align*}
4. \begin{align*}5m+2(7-6)\times 2^3 = 2^2 \times 4^2 +7\end{align*}
5. \begin{align*}3^2-2^2-15+3^3+2^3=f(2+1)-2\end{align*}

## Date Created:

Jan 18, 2013

Dec 29, 2014
Save or share your relevant files like activites, homework and worksheet.
To add resources, you must be the owner of the Modality. Click Customize to make your own copy.